Hi All,
We're told that the symbol # denotes one of the four arithmetic operations: addition, subtraction, multiplication, or division and that 6#3 <= 3. We're asked which of the three Roman Numerals must be true.
To start, let's do a bit of analysis on the inequality that we're given (and determine which math operation COULD fit this):
6#3 <= 3
6 + 3 = 9 which is NOT <= 3
6 - 3 = 3 which IS <= 3
(6)(3) = 18 which is NOT <= 3
6/3 = 2 which IS <=3
Thus, the symbol # must be either subtraction or division (although we don't know which one for sure).
I. 2#2 = 0
We've proven that the symbol is either subtraction or division, so let's see if either of those operations 'fits' this information...
2 - 2 = 0
2/2 = 1
Thus, if the symbol is subtraction, then Roman Numeral 1 IS true. However, if the symbol is division, then Roman Numeral 1 is NOT true. There's no way to know which symbol is involved though, so Roman Numeral 1 is not necessarily true.
Eliminate Answers A, D and E.
II. 2#2 = 1
With the work that we've done in Roman Numeral 1 (above), we already know that the outcome of 2#2 could be 0 or 1. This inconsistency also provides that Roman Numeral 2 is not necessarily true.
Eliminate Answer B.
There's only one answer remaining....
III. 4#2 = 2
You can still prove that Roman Numeral 3 is always true...
4 - 2 = 2
4/2 = 2
Both outcomes 'fit' the information in Fact 3, so regardless of what operation is represented, the statement IS true.
Final Answer:
GMAT assassins aren't born, they're made,
Rich